We would like to travel from Edinburgh by train to a large town in Wales where we can get get bus service around Wales. Any suggestion?
Where do you want to visit in Wales? Cross Wales travel is not always easy. It's the mountains you see. (Poor imitation of Dai Station I know, but I hope you get the real point ...)
My main question is what train do I take from Edinburgh Scotland to a large city in Wales?
There are three cities in Wales with a population of more than 100,000, Cardiff, Swansea and Newport. There are no direct trains to any of them from Scotland, so the most likely route would be the Virgin Trains service from Edinburgh Waverley to Birmingham New Street and change there to an Arriva Trains Wales service to Cardiff. Other routes are possible, so try www.nationalrail.co.uk for journey planning, but individual train operating company websites may give you special offers you won't find on National Rail. What you will notice is that all of those cities are in the south. Much of Wales is very rural and mountainous, and not densely populated. Marco's point is a good one - getting around in the rural interior is not easy, so if you mainly want to go to Snowdonia you probably wouldn't choose Cardiff or anywhere in the south as a base.
Shirley - You don't mention what time of year you will be traveling. Keep in mind if you are locked into specific dates, you can purchase you tickets early and save a few £'s. There is a train that departs Edinburgh at 9:08 and arrives Cardiff Central at 16:22 with a change in Bristol Parkway.
You really need to decide what it is that you want to see before you can get much help. Newport's a dud, Swansea is not much better, and Cardiff floats to the top only by default. Google something like 'rail map Wales' and you'll see that the only real north-south artery is in England. If you stay up north you can hit Conwy and Bangor, but to get as far west as Caernarvon, you're going to have to switch to a bus. Down south, you can get to a couple or three of the better castles before you have to come up with another idea for getting around.
The question is difficult because it is so broad. From southern Scotland to somewhere in Wales there are a number of possible routes, and within Wales the choices are so limited. As Ed so accurately said, the big towns in Wales are all right in the south and the places many people go to on holiday are often in the north, west or east of the Principality. Buses are limited in their scope because the transport takes so long due to the previously mentioned mountains all over Wales. Many people use towns or cities on the English side of the border for travel into the land of dragons. Places like Shrewsbury, Chester, Bristol, Gloucester. Each of those staging points is reached by a different train company or combination. Without a guide from you, Shirley, it is like throwing darts in the dark.
I'm now thinking of going to Conwy because after a visit in Wales we plan to visit Ireland and I see we can take a ferry to Dublin from near by Holyhead.
We are just going to Wales to mark it off our list of countries we have visited. Does that sound like a good plan?